Related papers: Component Evolution in General Random Intersection…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals' affected neighbors, such a spreading process becomes a "complex…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
In this paper, we introduce a novel model for random hypergraphs based on weighted random connection models. In accordance with the standard theory for hypergraphs, this model is constructed from a bipartite graph. In our stochastic model,…
We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
We analyse the scaling limit of the sizes of the largest components of the Random Intersection Graph $G(n,m,p)$ close to the critical point $p=\frac{1}{\sqrt{nm}}$, when the numbers $n$ of individuals and $m$ of communities have different…
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
Consider the complete graph \(K_n\) on \(n\) vertices where each edge \(e\) is independently open with probability \(p_n(e)\) or closed otherwise. Here \(\frac{C-\alpha_n}{n} \leq p_n(e) \leq \frac{C+\alpha_n}{n}\) where \(C > 0\) is a…
We study the number of chords and the number of crossings in the largest component of a random chord diagram when the chords are sparsely crossing. This is equivalent to studying the number of vertices and the number of edges in the largest…
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering…
Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…
Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete…
When dealing with evolving or multi-dimensional complex systems, network theory provides with elegant ways of describing their constituting components, through respectively time-varying and multi-layer complex networks. Nevertheless, the…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
Complex networks have non-trivial characteristics and appear in many real-world systems. Such networks are vitally important, but their full underlying dynamics are not completely understood. Utilizing new data sources, however, can unveil…
Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to…